Problem: Subtract $11b^2-4b+7$ from $b^2+8b-9$.
Answer: Since we are asked to subtract $11b^2-4b+7$ from $b^2+8b-9$, let's rewrite it as one expression. But how do we know which terms go where? Well, if we were asked to "subtract $13$ from $4$ ", we would rewrite it as $4 - 13$. In other words, we would start with $4$ and then subtract $13$. Let's use this pattern to rewrite the problem as one expression: ${(b^2+8b-9)-(11b^2-4b+7)}$ Since we are subtracting, it is helpful to distribute the $\text{{negative sign}}$ across all terms in the second trinomial: $\begin{aligned}&(b^2+8b-9){-}(11b^2-4b+7)\\ \\ =&(b^2+8b-9){-}11b^2{-}(-4b){-}7\\ \\ =&b^2+8b-9-11b^2+4b-7 \end{aligned}$ Note that the parentheses around the first trinomial don't affect the order of operations, so we can just remove them. When we add or subtract terms in a polynomial expression, the only way that we can simplify the expression is by combining those terms that are alike. Our expression contains terms of $3$ different degrees in the same variable: ${b^2}, {b},$ and the $\text{{constant}}$ term: ${{b^2} {+8b} {-9} {-11b^2} { +4b} {-7}}$ Note that there is an "invisible" coefficient of $1$ in front of the term ${b^2}$. Now that we have identified like terms, let's combine them. Make sure to keep track of positive and negative signs! ${{(1-11)b^2} + {(8+4)b} + {(-9-7)}}$ When we combine the coefficients in front of each term, we get the following trinomial: $-10b^2 +12b-16$